Search results for: Boundary layer equation

Authors: Xi Gu, Guan Heng Yeoh, Victoria Timchenko

Abstract:

In the current work, a three-dimensional geometry of a 75% stenosed blood vessel is analyzed. Large eddy simulation (LES) with the help of a dynamic subgrid scale Smagorinsky model is applied to model the turbulent pulsatile flow. The geometry, the transmural pressure and the properties of the blood and the elastic boundary were based on clinical measurement data. For the flexible wall model, a thin solid region is constructed around the 75% stenosed blood vessel. The deformation of this solid region was modelled as a deforming boundary to reduce the computational cost of the solid model. Fluid-structure interaction is realized via a twoway coupling between the blood flow modelled via LES and the deforming vessel. The information of the flow pressure and the wall motion was exchanged continually during the cycle by an arbitrary Lagrangian-Eulerian method. The boundary condition of current time step depended on previous solutions. The fluctuation of the velocity in the post-stenotic region was analyzed in the study. The axial velocity at normalized position Z=0.5 shows a negative value near the vessel wall. The displacement of the elastic boundary was concerned in this study. In particular, the wall displacement at the systole and the diastole were compared. The negative displacement at the stenosis indicates a collapse at the maximum velocity and the deceleration phase.

Keywords: Large Eddy Simulation, Fluid Structural Interaction, Constricted Artery, Computational Fluid Dynamics.

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Authors: H. Mohammadiun, A. Kianifar, A. Kargar

Abstract:

Nowadays, there is little information, concerning the heat shield systems, and this information is not completely reliable to use in so many cases. for example, the precise calculation cannot be done for various materials. In addition, the real scale test has two disadvantages: high cost and low flexibility, and for each case we must perform a new test. Hence, using numerical modeling program that calculates the surface recession rate and interior temperature distribution is necessary. Also, numerical solution of governing equation for non-charring material ablation is presented in order to anticipate the recession rate and the heat response of non-charring heat shields. the governing equation is nonlinear and the Newton- Rafson method along with TDMA algorithm is used to solve this nonlinear equation system. Using Newton- Rafson method for solving the governing equation is one of the advantages of the solving method because this method is simple and it can be easily generalized to more difficult problems. The obtained results compared with reliable sources in order to examine the accuracy of compiling code.

Keywords: Ablation rate, surface recession, interior temperaturedistribution, non charring material ablation, Newton Rafson method.

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Authors: Amrita Tripathi, Neeru Adlakha

Abstract:

Calcium [Ca2+] dynamics is studied as a potential form of neuron excitability that can control many irregular processes like metabolism, secretion etc. Ca2+ ion enters presynaptic terminal and increases the synaptic strength and thus triggers the neurotransmitter release. The modeling and analysis of calcium dynamics in neuron cell becomes necessary for deeper understanding of the processes involved. A mathematical model has been developed for cylindrical shaped neuron cell by incorporating physiological parameters like buffer, diffusion coefficient, and association rate. Appropriate initial and boundary conditions have been framed. The closed form solution has been developed in terms of modified Bessel function. A computer program has been developed in MATLAB 7.11 for the whole approach.

Keywords: Laplace Transform, Modified Bessel function, reaction diffusion equation, diffusion coefficient, excess buffer, calcium influx

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Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd Yatim

Abstract:

In this paper, a few chattering-free Sliding Mode Controllers (SMC) are proposed to stabilize an Active Magnetic Bearing (AMB) system with gyroscopic effect that is proportional to the rotor speed. The improved switching terms of the controller inherited from the saturation-type function and boundary layer control technique is shown to be able to achieve bounded and asymptotic stability, respectively, while the chattering effect in the input is attenuated. This is proven to be advantageous for AMB system since minimization of chattering results in optimized control effort. The performance of each controller is demonstrated via result of simulation in which the measurement of the total consumed energy and maximum control magnitude of each controller illustrates the effectiveness of the proposed controllers.

Keywords: Active Magnetic Bearing (AMB), Sliding Mode Control (SMC), chattering-free SMC.

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Authors: Zanariah Mohd Yusof, Siti Khuzaimah Soid, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

Abstract:

Unsteady magnetohydrodynamics (MHD) boundary layer flow and heat transfer over a continuously stretching surface in the presence of radiation is examined. By similarity transformation, the governing partial differential equations are transformed to a set of ordinary differential equations. Numerical solutions are obtained by employing the Runge-Kutta-Fehlberg method scheme with shooting technique in Maple software environment. The effects of unsteadiness parameter, radiation parameter, magnetic parameter and Prandtl number on the heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases as the Prandtl number and unsteadiness parameter increase but decreases with magnetic and radiation parameter.

Keywords: Heat transfer, magnetohydrodynamics, radiation, unsteadiness.

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Authors: Ahmed M. Farag, Wael F. Mohamed, Atef A. Ata, Burhamy M. Burhamy

Abstract:

In the present paper, an improved initial value numerical technique is presented to analyze the free vibration of symmetrically laminated rectangular plate. A combination of the initial value method (IV) and the finite differences (FD) devices is utilized to develop the present (IVFD) technique. The achieved technique is applied to the equation of motion of vibrating laminated rectangular plate under various types of boundary conditions. Three common types of laminated symmetrically cross-ply, orthotropic and isotropic plates are analyzed here. The convergence and accuracy of the presented Initial Value-Finite Differences (IVFD) technique have been examined. Also, the merits and validity of improved technique are satisfied via comparing the obtained results with those available in literature indicating good agreements.

Keywords: Free Vibrations, Initial Value, Finite Differences, Laminated plates.

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Authors: Ahmed A. D. Sarhan, Chong Feng Duan, Mum Wai Yip, M. Sayuti

Abstract:

Rapid Prototyping (RP) technologies enable physical parts to be produced from various materials without depending on the conventional tooling. Fused Deposition Modeling (FDM) is one of the famous RP processes used at present. Tensile strength and compressive strength resistance will be identified for different sample structures and different layer orientations of ABS rapid prototype solid models. The samples will be fabricated by a FDM rapid prototyping machine in different layer orientations with variations in internal geometrical structure. The 0° orientation where layers were deposited along the length of the samples displayed superior strength and impact resistance over all the other orientations. The anisotropic properties were probably caused by weak interlayer bonding and interlayer porosity.

Keywords: Building orientation, compression strength, rapid prototyping, tensile strength.

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Authors: Chuanjian Wang, Changfu Liu, Zhengde Dai

Abstract:

In this paper, the direct AnsAz method is used for constructing the multi-wave solutions to the (2+1)-dimensional extension of the Korteweg de-Vries (shortly EKdV) equation. A new breather type of three-wave solutions including periodic breather type soliton solution, breather type of two-solitary solution are obtained. Some cases with specific values of the involved parameters are plotted for each of the three-wave solutions. Mechanical features of resonance interaction among the multi-wave are discussed. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.

Keywords: EKdV equation, Breather, Soliton, Bilinear form, The direct AnsAz method.

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Authors: T. H. Young, Y. J. Tsai

Abstract:

A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work.  The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.

Keywords: Stress analysis, free vibration, plate buckling, nonuniform in-plane edge shear.

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

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Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter, functionally graded index and piezoelectric thickness on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Stability, Functionally graded beam, First order shear deformation theory, Piezoelectric layer.

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Authors: K. Kalaikumar, E. Baburaj

Abstract:

One of the problems to be addressed in wireless sensor networks is the issues related to cross layer communication. Cross layer architecture shares the information across the layer, ensuring Quality of Services (QoS). With this shared information, MAC protocol adapts effective functionality maintenance such as route selection on changeable sensor network environment. However, time slot assignment and neighbour route selection time duration for cross layer have not been carried out. The time varying physical layer communication over cross layer causes high traffic load in the sensor network. Though, the traffic load was reduced using cross layer optimization procedure, the computational cost is high. To improve communication efficacy in the sensor network, a self-determined time slot based Cross-Layered Neighbour Route Discovery (C-LNRD) method is presented in this paper. In the presented work, the initial process is to discover the route in the sensor network using Dynamic Source Routing based Medium Access Control (MAC) sub layers. This process considers MAC layer operation with dynamic route neighbour table discovery. Then, the discovered route path for packet communication employs Broad Route Distributed Time Slot Assignment method on Cross-Layered Sensor Network system. Broad Route means time slotting on varying length of the route paths. During packet communication in this sensor network, transmission of packets is adjusted over the different time with varying ranges for controlling the traffic rate. Finally, Rayleigh fading model is developed in C-LNRD to identify the performance of the sensor network communication structure. The main task of Rayleigh Fading is to measure the power level of each communication under MAC sub layer. The minimized power level helps to easily reduce the computational cost of packet communication in the sensor network. Experiments are conducted on factors such as power factor, on packet communication, neighbour route discovery time, and information (i.e., packet) propagation speed.

Keywords: Medium access control, neighbour route discovery, wireless sensor network, Rayleigh fading, distributed time slot assignment

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Authors: Yanling Zhu, Kai Wang

Abstract:

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g  t,  0 −τ x(t + s) dα(s)  + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.

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Authors: Nopparat Pochai, Rujira Deepana

Abstract:

Water pollution assessment problems arise frequently in environmental science. In this research, a finite difference method for solving the one-dimensional steady convection-diffusion equation with variable coefficients is proposed; it is then used to optimize water treatment costs.

Keywords: Finite difference, One-dimensional, Steady state, Waterpollution control, Optimization, Convection-diffusion equation.

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Authors: O. Frolov, K. Kolacek, J. Schmidt, J. Straus, V. Prukner, A. Shukurov

Abstract:

Many applications require surface modification and micro-structuring of polymers. For these purposes is mainly used ultraviolet (UV) radiation from excimer lamps or excimer lasers. However, these sources have a decided disadvantage - degrading the polymer deep inside due to relatively big radiation penetration depth which may exceed 100 μm. In contrast, extreme ultraviolet (EUV) radiation is absorbed in a layer approximately 100 nm thick only. In this work, the radiation from a discharge-plasma EUV source (with wavelength 46.9 nm) based on a capillary discharge driver is focused with a spherical Si/Sc multilayer mirror for surface modification of PMMA sample or thin gold layer (thickness about 40 nm). It was found that the focused EUV laser beam is capable by one shot to ablate PMMA or layer of gold, even if the focus is significantly influenced by astigmatism.

Keywords: ablation, capillary discharge, EUV laser, surface modification

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Authors: Ram N. Singh, Abraham K. George, Dawood N. Al-Namaani

Abstract:

The Euler-s equation of motion is extended to include the viscosity stress tensor leading to the formulation of Navier– Stokes type equation. The latter is linearized and applied to investigate the rotational motion or vorticity in a viscous fluid. Relations for the velocity of viscous waves and attenuation parameter are obtained in terms of viscosity (μ) and the density (¤ü) of the fluid. μ and ¤ü are measured experimentally as a function of temperature for two different samples of light and heavy crude oil. These data facilitated to determine the activation energy, velocity of viscous wave and the attenuation parameter. Shear wave velocity in heavy oil is found to be much larger than the light oil, whereas the attenuation parameter in heavy oil is quite low in comparison to light one. The activation energy of heavy oil is three times larger than light oil.

Keywords: Activation Energy, Attenuation, Crude Oil, Navier- Stokes Equation, Viscosity.

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Authors: Renata L. C. Leão, João E. Nascimento, Natalia C. E. S. Nascimento, Elaine S. Vasconcelos, Mércia L. Oliveira

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The quality control procedures of a radiopharmaceutical include the assessment of its chemical purity. The method suggested by international pharmacopeias consists of a thin layer chromatographic run. In this paper, the method proposed by the United States Pharmacopeia (USP) is compared to a direct method to determine the final concentration of aminopolyether in Fludeoxyglucose (¹⁸F-FDG) preparations. The approach (no chromatographic run) was achieved by placing the thin-layer chromatography (TLC) plate directly on an iodine vapor chamber. Both methods were validated and they showed adequate results to determine the concentration of aminopolyether in ¹⁸F-FDG preparations. However, the direct method is more sensitive, faster and simpler when compared to the reference method (with chromatographic run), and it may be chosen for use in routine quality control of ¹⁸F-FDG.

Keywords: Chemical purity, Kryptofix 222, thin layer chromatography, validation.

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Authors: A. Pourahmad, Sh. Gharipour

Abstract:

The present work describes the preparation and characterization of nanosized SiO₂@PbS core-shell particles by using a simple wet chemical route. This method utilizes silica spheres formation followed by successive ionic layer adsorption and reaction method assisted lead sulphide shell layer formation. The final product was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), UV–vis spectroscopic, infrared spectroscopy (IR) and transmission electron microscopy (TEM) experiments. The morphological studies revealed the uniformity in size distribution with core size of 250 nm and shell thickness of 18 nm. The electron microscopic images also indicate the irregular morphology of lead sulphide shell layer. The structural studies indicate the face-centered cubic system of PbS shell with no other trace for impurities in the crystal structure.

Keywords: Core-shell, nanostructure, semiconductor, optical property, XRD.

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Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Mansour Nikkhah-Bahrami, Masih Loghmani, Mostafa Pooyanfar

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In this paper, an analytical approach for free vibration analysis of four edges simply supported rectangular Kirchhoff plates is presented. The method is based on wave approach. From wave standpoint vibration propagate, reflect and transmit in a structure. Firstly, the propagation and reflection matrices for plate with simply supported boundary condition are derived. Then, these matrices are combined to provide a concise and systematic approach to free vibration analysis of a simply supported rectangular Kirchhoff plate. Subsequently, the eigenvalue problem for free vibration of plates is formulated and the equation of plate natural frequencies is constructed. Finally, the effectiveness of the approach is shown by comparison of the results with existing classical solution.

Keywords: Kirchhoff plate, propagation matrix, reflection matrix, vibration analysis.

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Authors: Chia-Ling Chang, Chung-Sheng Liao

Abstract:

The present study focuses on the discussion over the parameter of Artificial Neural Network (ANN). Sensitivity analysis is applied to assess the effect of the parameters of ANN on the prediction of turbidity of raw water in the water treatment plant. The result shows that transfer function of hidden layer is a critical parameter of ANN. When the transfer function changes, the reliability of prediction of water turbidity is greatly different. Moreover, the estimated water turbidity is less sensitive to training times and learning velocity than the number of neurons in the hidden layer. Therefore, it is important to select an appropriate transfer function and suitable number of neurons in the hidden layer in the process of parameter training and validation.

Keywords: Artificial Neural Network (ANN), sensitivity analysis, turbidity.

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Authors: Pankaj Kumar Srivastava

Abstract:

Bringing forth a survey on recent higher order spline techniques for solving boundary value problems in ordinary differential equations. Here we have discussed the summary of the articles since 2000 till date based on higher order splines like Septic, Octic, Nonic, Tenth, Eleventh, Twelfth and Thirteenth Degree splines. Comparisons of methods with own critical comments as remarks have been included.

Keywords: Septic spline, Octic spline, Nonic spline, Tenth, Eleventh, Twelfth and Thirteenth Degree spline, parametric and non-parametric splines, thermal instability, astrophysics.

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Authors: Minghui Wang, Juntao Zhang

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An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.

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Authors: R. Karmouch

Abstract:

A thin gold metal layer was deposited on the top of silicon oxide films containing embedded Si nanocrystals (Si-nc). The sample was annealed in a gas containing nitrogen, and subsequently characterized by photoluminescence. We obtained 3-fold enhancement of photon emission from the Si-nc embedded in silicon dioxide covered with a Gold layer as compared with an uncovered sample. We attribute this enhancement to the increase of the spontaneous emission rate caused by the coupling of the Si-nc emitters with the surface plasmons (SP). The evolution of PL emission with laser irradiated time was also collected from covered samples, and compared to that from uncovered samples. In an uncovered sample, the PL intensity decreases with time, approximately with two decay constants. Although the decrease of the initial PL intensity associated with the increase of sample temperature under CW pumping is still observed in samples covered with a gold layer, this film significantly contributes to reduce the permanent deterioration of the PL intensity. The resistance to degradation of light-emitting silicon nanocrystals can be increased by SP coupling to suppress the permanent deterioration. Controlling the permanent photodeterioration can allow to perform a reliable optical gain measurement.

Keywords: Photodeterioration, Silicon Nanocrystals, Ion Implantation, Photoluminescence, Surface Plasmons.

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

Abstract:

This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Functionally Graded Beam, Free Vibration, Elastic Foundation, Engesser-Timoshenko Beam Theory.

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Authors: Huei-Fu Lu

Abstract:

This study links up the theories of social psychology, economics and sport management to assess the impact of sport participation on subjective well-being (SWB) and use a simple statistic method to estimate the relative monetary value that sport participation derives SWB for Taiwan-s college students. By constructing proper measurements on sport participation and SWB respectively, a structural equation model (SEM) is developed to perform a confirmatory factory analysis, and the causal relationship between sport participation and SWB as well as the effect of the demographic variables on these two concepts are also discussed.

Keywords: Demographics, Economic value, Sport participation, Structural equation modeling (SEM), Subjective well-being.

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Authors: Yakin Hajlaoui, Richard Labib, Jean-Franc¸ois Plante, Michel Gamache

Abstract:

This study presents the Multi-Layer Inverse Distance Weighting Model (ML-IDW), inspired by the mathematical formulation of both multi-layer neural networks (ML-NNs) and Inverse Distance Weighting model (IDW). ML-IDW leverages ML-NNs’ processing capabilities, characterized by compositions of learnable non-linear functions applied to input features, and incorporates IDW’s ability to learn anisotropic spatial dependencies, presenting a promising solution for nonlinear spatial interpolation and learning from complex spatial data. We employ gradient descent and backpropagation to train ML-IDW. The performance of the proposed model is compared against conventional spatial interpolation models such as Kriging and standard IDW on regression and classification tasks using simulated spatial datasets of varying complexity. Our results highlight the efficacy of ML-IDW, particularly in handling complex spatial dataset, exhibiting lower mean square error in regression and higher F1 score in classification.

Keywords: Deep Learning, Multi-Layer Neural Networks, Gradient Descent, Spatial Interpolation, Inverse Distance Weighting.

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Authors: C. Panya-Isara, T. Kulworawanichpong, P. Pao-La-Or

Abstract:

Piezoelectric transformers are electronic devices made from piezoelectric materials. The piezoelectric transformers as the name implied are used for changing voltage signals from one level to another. Electrical energy carried with signals is transferred by means of mechanical vibration. Characterizing in both electrical and mechanical properties leads to extensively use and efficiency enhancement of piezoelectric transformers in various applications. In this paper, study and analysis of electrical and mechanical properties of multi-layer piezoelectric transformers in forms of potential and displacement distribution throughout the volume, respectively. This paper proposes a set of quasi-static mathematical model of electromechanical coupling for piezoelectric transformer by using a set of partial differential equations. Computer-based simulation utilizing the three-dimensional finite element method (3-D FEM) is exploited as a tool for visualizing potentials and displacements distribution within the multi-layer piezoelectric transformer. This simulation was conducted by varying a number of layers. In this paper 3, 5 and 7 of the circular ring type were used. The computer simulation based on the use of the FEM has been developed in MATLAB programming environment.

Keywords: Multi-layer Piezoelectric Transformer, 3-D Finite Element Method (3-D FEM), Electro-mechanical Coupling, Mechanical Vibration

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Authors: Li Long, Thomas Ortlepp

Abstract:

The transport properties of carriers in polycrystalline silicon film affect the performance of polycrystalline silicon-based devices. They depend strongly on the grain structure, grain boundary trap properties and doping concentration, which in turn are determined by the film deposition and processing conditions. Based on the properties of charge carriers, phonons, grain boundaries and their interactions, the thermoelectric properties of polycrystalline silicon are analyzed with the relaxation time approximation of the Boltzmann transport equation. With this approach, thermal conductivity, electrical conductivity and Seebeck coefficient as a function of grain size, trap properties and doping concentration can be determined. Experiment on heavily doped polycrystalline silicon is carried out and measurement results are compared with the model.

Keywords: Conductivity, polycrystalline silicon, relaxation time approximation, Seebeck coefficient, thermoelectric property.

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Authors: Fatma Ghangir, Andrzej F. Nowakowski, Franck C. G. A. Nicolleau, Thomas M. Michelitsch

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The performance of high-resolution schemes is investigated for unsteady, inviscid and compressible multiphase flows. An Eulerian diffuse interface approach has been chosen for the simulation of multicomponent flow problems. The reduced fiveequation and seven equation models are used with HLL and HLLC approximation. The authors demonstrated the advantages and disadvantages of both seven equations and five equations models studying their performance with HLL and HLLC algorithms on simple test case. The seven equation model is based on two pressure, two velocity concept of Baer–Nunziato [10], while five equation model is based on the mixture velocity and pressure. The numerical evaluations of two variants of Riemann solvers have been conducted for the classical one-dimensional air-water shock tube and compared with analytical solution for error analysis.

Keywords: Multiphase flow, gas-liquid flow, Godunov schems, Riemann solvers, HLL scheme, HLLC scheme.

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Authors: Yanqin Chen, Chao Jiang, Chongdu Cho

Abstract:

This research presents the three-dimensional mechanical characteristics of a commercial gas diffusion layer by experiment and simulation results. Although the mechanical performance of gas diffusion layers has attracted much attention, its reliability and accuracy are still a major challenge. With the help of simulation analysis methods, it is beneficial to the gas diffusion layer’s extensive commercial development and the overall stress analysis of proton electrolyte membrane fuel cells during its pre-production design period. Therefore, in this paper, a three-dimensional constitutive model of a commercial gas diffusion layer, including its material stiffness matrix parameters, is developed and coded, in the user-defined material model of a commercial finite element method software for simulation. Then, the model is validated by comparing experimental results as well as simulation outcomes. As a result, both the experimental data and simulation results show a good agreement with each other, with high accuracy.

Keywords: Gas diffusion layer, proton electrolyte membrane fuel cell, stiffness matrix, three-dimensional mechanical characteristics, user-defined material model.

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